Comparative Performance of Mamdani and Sugeno Fuzzy Inference Systems with Gaussian Membership Functions for Mathematics Learning Assessment

Abstract

Fuzzy inference systems (FISs) provide a framework for modelling the gradual and uncertain nature of student learning achievement. This study presents a controlled comparison of Mamdani and Sugeno fuzzy inference systems using Gaussian membership functions for mathematics learning assessment. The comparison retains the same dataset, input variables, Gaussian membership functions, and expert-defined rule base while changing only the inference mechanism. The dataset comprises 360 secondary school students, with examination score, assignment completion, and class participation used as input variables and teacher evaluation used as the benchmark for learning achievement. Both systems employ three Gaussian linguistic terms for each input and the same 27-rule knowledge base, while a zeroth-order Sugeno formulation is used for the Sugeno model. Model performance is evaluated using Pearson correlation coefficient, root mean square error (RMSE), and mean absolute error (MAE). Under the present dataset and model configuration, the Sugeno-Gaussian FIS achieved a Pearson correlation of 0.98996, RMSE of 2.7651, and MAE of 2.4279, compared with 0.9623, 7.2630, and 6.5607, respectively, for the Mamdani-Gaussian FIS. The results indicate that the Sugeno-Gaussian model achieved stronger linear agreement with teacher evaluations and lower prediction errors than the Mamdani-Gaussian model under the controlled conditions examined. These findings suggest that the choice of inference mechanism can influence the numerical performance of fuzzy-based mathematics learning assessment, although the results are limited to the dataset, rule base, membership-function configuration, and modelling assumptions considered in this study